<HYPERELASTICITY> modified_sv_kirchhoff#

Description#

This hyperelastic model is a modified St Venant-Kirchhoff model [M13], which is defined by the following strain energy \(W\):

\[W(\ten E)=\dfrac{\lambda}{2}(\log{J})^2+\mu~tr(\ten E^2)\]

where \(\lambda\) and \(\mu\) are Lamé coefficients in the infinitesimal elasticity theory, E is the Green-Lagrange strain tensor and \(J=det \ten F\). The second Piola-Kirchhoff stress tensor can be obtained as

\[\ten S=\dfrac{dW}{d \ten E}=\lambda\log(J)\ten C^{-1}+2\mu \ten E\]

where \(ten C\) is the right Cauchy-Green deformation tensor. This model overcomes the limits of St Venant-kirchhoff ones.

../../_images/hyper_mat.svg

Syntax#

***behavior hyper_elastic \(~\,\) **hyperelasticity modified_sv_kirchhoff \(~\,~\,\) *elasticity \(~\,~\,~\,\) young COEFFICIENT \(~\,~\,~\,\) poisson COEFFICIENT

Example#

The user can supply either \((\lambda,\mu)\) or \((E,\nu)\).

***behavior hyper_elastic
 **hyperelasticity modified_sv_kirchhoff
  *elasticity
    mu           80000.
    lambda       121000.
***return